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chore(kernel/quot): avoid legacy code

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This commit is contained in:
Leonardo de Moura 2018-06-09 07:54:45 -07:00
parent d5c24806e7
commit c632123fd1
1 changed files with 22 additions and 20 deletions
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42
src/kernel/quot.cpp
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@ -8,7 +8,7 @@ Quotient types.
*/
#include "kernel/old_type_checker.h"
#include "kernel/quot.h"
#include "kernel/abstract.h"
#include "kernel/local_ctx.h"
#include "kernel/inductive/inductive.h"
namespace lean {
@ -27,15 +27,16 @@ static void check_eq_type(environment const & env) {
if (!decl) throw exception("failed to initialize quot module, environment does not have 'eq' type");
if (length(decl->m_level_params) != 1)
throw exception("failed to initialize quot module, unexpected number of universe params at 'eq' type");
local_ctx lctx;
level u = mk_param_univ(head(decl->m_level_params));
expr alpha = mk_local("α", "α", mk_sort(u), mk_implicit_binder_info());
expr expected_eq_type = Pi(alpha, mk_arrow(alpha, mk_arrow(alpha, mk_Prop())));
expr alpha = lctx.mk_local_decl("α", "α", mk_sort(u), mk_implicit_binder_info());
expr expected_eq_type = lctx.mk_pi(alpha, mk_arrow(alpha, mk_arrow(alpha, mk_Prop())));
if (decl->m_type != expected_eq_type)
throw exception("failed to initialize quot module, 'eq' has an expected type");
if (length(decl->m_intro_rules) != 1)
throw exception("failed to initialize quot module, unexpected number of constructors for 'eq' type");
expr a = mk_local("a", alpha);
expr expected_eq_refl_type = Pi(alpha, Pi(a, mk_app(mk_constant("eq", {u}), alpha, a, a)));
expr a = lctx.mk_local_decl("a", alpha);
expr expected_eq_refl_type = lctx.mk_pi({alpha, a}, mk_app(mk_constant("eq", {u}), alpha, a, a));
if (mlocal_type(head(decl->m_intro_rules)) != expected_eq_refl_type) {
throw exception("failed to initialize quot module, unexpected type for 'eq' type constructor");
}
@ -45,44 +46,45 @@ environment quot_declare(environment const & env) {
check_eq_type(env);
environment new_env = env;
name u_name("u");
local_ctx lctx;
level u = mk_param_univ(u_name);
expr Sort_u = mk_sort(u);
expr alpha = mk_local("α", "α", Sort_u, mk_implicit_binder_info());
expr r = mk_local("r", mk_arrow(alpha, mk_arrow(alpha, mk_Prop())));
expr alpha = lctx.mk_local_decl("α", "α", Sort_u, mk_implicit_binder_info());
expr r = lctx.mk_local_decl("r", mk_arrow(alpha, mk_arrow(alpha, mk_Prop())));
/* constant {u} quot {α : Sort u} (r : α → α → Prop) : Sort u */
new_env = add_constant(new_env, *quot_consts::g_quot, {u_name}, Pi(alpha, Pi(r, Sort_u)));
new_env = add_constant(new_env, *quot_consts::g_quot, {u_name}, lctx.mk_pi({alpha, r}, Sort_u));
expr quot_r = mk_app(mk_constant(*quot_consts::g_quot, {u}), alpha, r);
expr a = mk_local("a", alpha);
expr a = lctx.mk_local_decl("a", alpha);
/* constant {u} quot.mk {α : Sort u} (r : α → α → Prop) (a : α) : @quot.{u} α r */
new_env = add_constant(new_env, *quot_consts::g_quot_mk, {u_name},
Pi(alpha, Pi(r, Pi(a, quot_r))));
lctx.mk_pi({alpha, r, a}, quot_r));
/* make r implicit */
r = mk_local("r", "r", mk_arrow(alpha, mk_arrow(alpha, mk_Prop())), mk_implicit_binder_info());
r = lctx.mk_local_decl("r", "r", mk_arrow(alpha, mk_arrow(alpha, mk_Prop())), mk_implicit_binder_info());
name v_name("v");
level v = mk_param_univ(v_name);
expr Sort_v = mk_sort(v);
expr beta = mk_local("β", "β", Sort_v, mk_implicit_binder_info());
expr f = mk_local("f", mk_arrow(alpha, beta));
expr b = mk_local("b", alpha);
expr beta = lctx.mk_local_decl("β", "β", Sort_v, mk_implicit_binder_info());
expr f = lctx.mk_local_decl("f", mk_arrow(alpha, beta));
expr b = lctx.mk_local_decl("b", alpha);
expr r_a_b = mk_app(r, a, b);
/* f a = f b */
expr f_a_eq_f_b = mk_app(mk_constant("eq", {v}), beta, mk_app(f, a), mk_app(f, b));
/* (∀ a b : α, r a b → f a = f b) */
expr sanity = Pi(a, Pi(b, mk_arrow(r_a_b, f_a_eq_f_b)));
expr sanity = lctx.mk_pi({a, b}, mk_arrow(r_a_b, f_a_eq_f_b));
/* constant {u v} quot.lift {α : Sort u} {r : α → α → Prop} {β : Sort v} (f : α → β)
: (∀ a b : α, r a b → f a = f b) → @quot.{u} α r → β */
new_env = add_constant(new_env, *quot_consts::g_quot_lift, {u_name, v_name},
Pi(alpha, Pi(r, Pi(beta, Pi(f, mk_arrow(sanity, mk_arrow(quot_r, beta)))))));
lctx.mk_pi({alpha, r, beta, f}, mk_arrow(sanity, mk_arrow(quot_r, beta))));
/* {β : @quot.{u} α r → Prop} */
beta = mk_local("β", "β", mk_arrow(quot_r, mk_Prop()), mk_implicit_binder_info());
beta = lctx.mk_local_decl("β", "β", mk_arrow(quot_r, mk_Prop()), mk_implicit_binder_info());
expr quot_mk_a = mk_app(mk_constant(*quot_consts::g_quot_mk, {u}), alpha, r, a);
expr all_quot = Pi(a, mk_app(beta, quot_mk_a));
expr q = mk_local("q", quot_r);
expr all_quot = lctx.mk_pi(a, mk_app(beta, quot_mk_a));
expr q = lctx.mk_local_decl("q", quot_r);
expr beta_q = mk_app(beta, q);
/* constant {u} quot.ind {α : Sort u} {r : α → α → Prop} {β : @quot.{u} α r → Prop}
: (∀ a : α, β (@quot.mk.{u} α r a)) → ∀ q : @quot.{u} α r, β q */
new_env = add_constant(new_env, *quot_consts::g_quot_ind, {u_name},
Pi(alpha, Pi(r, Pi(beta, mk_arrow(all_quot, Pi(q, beta_q))))));
lctx.mk_pi({alpha, r, beta}, mk_arrow(all_quot, lctx.mk_pi(q, beta_q))));
return new_env;
}